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Generalized Spectral Theory and Second Order Ordinary Differential Operators

  • Héctor J. Sussmann (a1)

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This paper continues the study, begun in [7], of the spectral theory of non-self-ad joint second order ordinary differential operators on a half-line. The case of a ‘Very small” potential was studied in [4; 5; 6]. The case considered in [7], and in the present paper, is that where the potential is not so small.

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References

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1. Colojoara, I. and Foias, C., Theory of generalized spectral operators (Gordon and Breach, New York, 1968).
2. Dunford, N., A survey of the theory of spectral operators, Bull. Amer. Math. Soc. 64 (1958), 217274.
3. Dunford, N. and Schwartz, J., Linear operators, Vol. 1 (Interscience, New York, 1958).
4. Dunford, N. and Schwartz, J., Linear operators, Vol. 3 (Interscience, to appear).
5. Ljance, V. E., A differential operator with spectral singularities. I, Mat. Sb. 64 (1964), 521-561 ; II, Mat. Sb. 65 (1964), 47109 (Russian).
6. Dunford, N. and Schwartz, J., Expansion in principal functions of an operator with spectral singularities, Rev. Roumaine Math. Pures Appl. 11 (1966), 921950 and 1187-1224 (Russian).
7. Sussmann, H. J., Non-spectrality of a class of second order ordinary differential operators, Comm. Pure Appl. Math. 23 (1970), 819840.
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Generalized Spectral Theory and Second Order Ordinary Differential Operators

  • Héctor J. Sussmann (a1)

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